Question: Given $ m \angle MON = 2x + 6$, and $ m \angle LOM = 3x + 99$, find $m\angle LOM$. $O$ $L$ $N$ $M$
Solution: From the diagram, we see that together ${\angle LOM}$ and ${\angle MON}$ form ${\angle LON}$ , so $ {m\angle LOM} + {m\angle MON} = {m\angle LON}$ Since $\angle LON$ is a straight angle, we know ${m\angle LON = 180}$ Substitute in the expressions that were given for each measure: $ {3x + 99} + {2x + 6} = {180}$ Combine like terms: $ 5x + 105 = 180$ Subtract $105$ from both sides: $ 5x = 75$ Divide both sides by $5$ to find $x$ $ x = 15$ Substitute $15$ for $x$ in the expression that was given for $m\angle LOM$ $ m\angle LOM = 3({15}) + 99$ Simplify: $ {m\angle LOM = 45 + 99}$ So ${m\angle LOM = 144}$.